International Journal of Scientific Engineering and Science Volume 3, Issue 2, pp. 20-25, 2019. ISSN (Online): 2456-7361 20 http://ijses.com/ All rights reserved Performance Analysis of Phase Estimation Algorithms for Interferometric Data Dr. M. M. Mohamed Ismail 1 , Dr. M. M. Mohamed Sathik 2 1 Assistant Professor, Department of Computer Applications, The New College, Chennai 2 Principal, Sadakathullah Appa College, Tirunelveli Email address: mohammedismi @gmail. com Abstract—Atmospheric turbulence strongly affects the performance of ground based telescope images. Shearing Interferometry based wavefront sensor is widely used for atmospheric turbulence correction in adaptive optics systems. In this paper, we simulated a noisy interferometric image based on polarized shearing interferometer which is affected by Kolmogorov turbulence. The phase extraction from noisy interferometric fringe pattern using different transform methods are described. The principles of Fourier transform (FT), windowed Fourier transform (WFT) and wavelet transform (WT) methods for phase extraction are discussed. Keywords— Adaptive Optics, Shearing Interferometer, Fourier transform, windowed Fourier transform and wavelet transform. I. INTRODUCTION In Astronomical Instrumentation, the medium is the Earth’s turbulent atmosphere, and the optical signal is the light emitted by the star or the body of interest. The atmospheric turbulence can be considered as a random process and can be estimated by means of variances and co-variances of local refractive index fluctuations [1]. Due to change in the refractive indices of the different layers, the planar wavefront, from the distant star, propagating through the turbulent atmosphere, gets distorted. So, both the amplitude and phase of the incoming beam fluctuate during its passage and changes with time. Thus, the random process of the atmospheric turbulence, affect the image forming capabilities of the telescope. The effects of turbulence on light that passes through the atmosphere are three types. a. It creates intensity fluctuations or scintillations which are observed as the twinkling of the stars. b. The position of the star wanders when the varying refractive index of the atmosphere alters the angle of arrival of the starlight. c. There is a spreading effect created by the higher order aberrations which causes stars to appear as small discs of light and not sharply defined point sources. To resolve atmospheric turbulence for ground based telescope, Adaptive Optics (AO) technology was developed by astronomers [2,3]. It is a technique which measures the wavefront phase errors generated by the variations of the index of refraction in the atmosphere and corrects the resulting image in real time to achieve an angular resolution close to the diffraction limits of the telescope. The major components involved in a simple Adaptive Optics system are Wavefront Sensor which measures phase variations, Wavefront Correction device (Deformable Mirror), control algorithm and hardware which must be very fast to correct real-time variations. A Wavefront Sensor is a device that helps in determining the shape of the incoming beam. Wavefront Corrector is a phase distortion compensation tool. The control algorithm takes the input from the Wavefront Sensor and translates the information into command values that can be addressed to the Wavefront Corrector. Various Wavefront Sensing techniques have been developed for use in a variety of applications ranging from measuring the wavefront aberrations of human eyes [4] to Adaptive Optics in astronomy [5]. The most commonly used Wavefront Sensors are the Shack-Hartmann (SH) [6, 7], Curvature sensing [8], Lateral Shearing Interferometry (LSI) [9, 10 and 11], Phase Retrieval methods [12] and Pyramid Wavefront Sensor [13]. It is important to understand the Polarization Shearing Interferometer (PSI) theoretically to sense the wavefront errors. For this purpose, a simulation of wavefront has been generated and incorporated the wavefront errors caused due to atmospheric turbulence. II. SIMULATION OF NOISY INTERFEROMETRIC FRINGE PATTERN Based on equation given 2.1 and which is explained at [14] an interferometric image was simulated as shown in figure 1.         2 2 2 2 2 2 2 2 2 , ( ) 3 W xy Ax y By x y Cx y Dx y Ey Fx           (2.1) Fig. 1. Typical Polarization Shearing Interferogram Gaussian noise is evenly distributed over the signal. This means that each pixel in the noisy image is the sum of the true pixel value and a random Gaussian distributed noise value. As the name indicates, this type of noise has a Gaussian